Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,bin R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpotent elements‎, ‎introducing‎ the concept of commutativity of nilpotent elements at zero (simply‎, ‎a CNZ ring)‎. ‎In this paper‎, ‎we extend the CNZ pr...

The challenge in developing oral drug delivery systems of poorly soluble basic drugs is primarily due to their pH dependent solubility. Cinnarizine (CNZ), a model for a poorly soluble basic drug, has pH dependent solubility; where it dissolves readily at low pH in the stomach and exhibits a very low solubility at pH values greater than 4. It is also characterized by a short half life of 3-6h, w...

To study the anomalous heat effect of Nibased binary-metal-nano-powder samples by gas-phase hydrogen isotope absorption/desorption, three kinds of samples CNZ, CNZ-II and NZ were tested for the temperature range 300-573 K. The highest excess heat power, ca. 2W/g-Ni was obtained with CNZ at 573 K. Peculiar H(D)-isotopic effect and sudden heat sink by abrupt H(D)-desorption were observed. The hea...

Discrete analytic functions are coinplex valued functions defined at points of the z-plane with integer coordinates. The real and imaginary parts of these functions are required to satisfy difference equations analogous to the Cauchy-Riemann equations. The pseudo power z() is a discrete analytic function which is asymptotic to the ordinary power z for large z. The central topic of this paper is...

We exhibit a sequence cn such that the convergence of ∑ n≥1 cnz n for |z| < 1 is equivalent to the Riemann Hypothesis. We argue that this particular RH-equivalent problem is “better” than most, or perhaps every, other RH-equivalent problem devised so far, in the sense that (we prove) there is a tremendous gap in behaviors of the cn if the RH is true versus if the RH is false.

Strong asymptotic results for relativistic Hermite polynomials H n (z) are established as n, N →∞, thereby supplementing recent results on weak asymptotics for these polynomials. Depending on growth properties of the ratio N/n for the rescaled polynomials H n (cnz) (cn being suitable positive numbers, n, N →∞), formulae of Plancherel-Rotach type are derived on the oscillatory interval, in the c...